# Formula for Evaluating Square Routes?

Is there a formula for finding the square route of a number without a calculator? If so, what is it, and please explain how to work it.

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• Anonymous

There is no formula but there are several ways to do it. Perhaps you know the one taught in high school. I will give you another. I will demonstrate it with a number N = 93

First take a number that might be close to the actual root. I take a = 9 since 9 * 9 < 93 < 10 * 10. But you can take anything from 1 to 92. Naturally taking a number closer to the real root will give you much quicker results. a = 10 is also a good choice.

Now calculate b = (a + N/a)/2 = (9 + 93/9)/2 = 9.67...

Now similarly calculate c = (b + N/b)/2 = (9.67 + 93/9.67)/2 = 9.64...

A third step will give you d = (c + N/c) = (9.64 + 93/9.64)/2 = 9.6436....

The actual root of 93 is approx 9.6437 and yet with just two steps we have got an answer that is correct to 2 decimal places, and an answer correct to 3 decimal places with 3 steps.

The advantage of this method is that YOU decide how many decimal places you want and how many times you want to carry out the steps. As long as the initial number a is properly chosen, you wont be far off from the real root.

If you practice a little, you can get very good and very fast at it. Hope this helps.

• Anonymous
4 years ago

1) 4*(square Root of 5) 2)a) b) c) You mistyped the function of g(x) 3)a)3p to the 7q root b) Mistype In parenthesis?, and the sign for multiply is * c)Again were are Parenthesis, if none, then 3q^4 d)r^5 3)part2? a)(x+4)(x+3) b)(7x-4)(7x+4) 4) I'm way to lazy to plug and chug at the quadratic equations. You need to learn this stuff, This is the basics from which nearly everything i do is formed from. Try to figure them out and see if you get the same answers. If you get to algebra II with out fully understanding this stuff. then your in for a long ride.

• find the two nearest perfect squares and estimate in the middle